Lattice fermions at non-zero temperature and chemical potential

We study the free fermion gas at finite temperature and chemical potential in the lattice regularized version proposed by Hasenfratz and Karsch and by Kogut et al. Special emphasis is placed on the identification of the particle and antiparticle contributions to the partition function. In the case of naive fermions we show that the partition function no longer separates into particle-antiparticle contributions in the way familiar from the continuum formulation. The use of Wilson fermions, on the other hand, eliminates this unpleasant feature, and leads, after subtracting the vacuum contributions, to the familiar expressions for the average energy and charge densities.     

Failure of the naïve loop expansion for the effective potential in φ4 field theory when there is “broken symmetry”

We determine the effective potential V[φ] in zero dimensional gφ⁴ field theory when there is broken symmetry classically $\text{[V}{}_{\mathrm{<mtext>cl</mtext>}}\text{=}\text{1}\text{4}\text{g(φ}{}^2\text{? a}{}^2\text{)}{}^2\text{]}$ as a power series in 1/g. We find that the usual loop expansion ignores a secondary minimum of the path integral and is only valid for |φ| ? a.When |ja| ? 1, where j is the external source, there is a secondary minimum of equal importance to the absolute minimum. In that region a kink solution to the differential equation for φ[j] exists, φ[j] = a tanh(ja) + O(ja²/ga⁴), which interpolates between the minima at φ = ?a and φ = +a. We obtain the 1/g expansion for V[φ] for φ < a and φ ? a. For all g, a mean-field approximation gives an expression for V[φ] which interpolates between these two regimes. In higher dimensions the kink solution becomes $\text{φ[j] = a}\text{tanh}\text{(jaΩ)}$, where Ω is the volume of space-time, suggesting a discontinuity in φ[j] in the infinite-volume limit.     

Polar Substituents in Benzobarrelene Photochemistry; The Photoreactivities of Dimethyl 10-methoxy- and Dimethyl 10,11-dimethoxy-2,3-benzobicyclo[2.2.2]octateraene-5,6-dicarboxylate

The direct irradiation of the monomethoxybarrelene 8 gives cyclooctatetraene product 18 (Φ = 0.075) via the anti-Epiotis aromatic-vinyldiester [2π+2π] bridging route, and two semibullvalenes 16 (Φ = 0.075) and 17 (Φ = 0.075) from di-π-methane rearrangements initiating from vinyl-vinyldiester bridging. Benzophenone sensitization yields 16 (Φ =0.11) and 17 (Φ = 0.11). The dimethoxybarrelene 9 gives only semibullvalene 10 , this resulting from di-π-methane rearrangement involving the vinyl and vinyldiester bridges, upon direct (Φ = 0.009) or benzophenone sensitized irradiations (Φ = 0.38). 10 undergoes a vinylcyclopropane rearrangement to give semibullvalene 11 upon direct or acetone sensitized irradiations (Φ = 0.008).     

Prediction of Re ɛ fromK 13 decays in an extended cabibbo model

With the help of an extended Cabibbo model for the weak hadronic vector current which includes the 10 and ¯10 representations to account for possibleΔS=-ΔQ transitions, a prediction is made for the quantity (1-¦x¦²)/¦1?x¦² wherex=A(K⁰→π^üe^?¯v)/A(¯K⁰→π^üe^?¯v) using the experimental branching ratio Γ(K^?→ π⁰e^?¯v/Γ(K _L ⁰ →π^üe^?¯v). From the known charge asymmetry in the decay of the long lived kaon one then obtains Re?.     

Electrical properties of bilayer lipid membranes containing iodine and iodide,investigated by cyclic voltammetry

The conduction properties of lecithin bilayer membranes in iodine-containing solutions are examined from a potentiodynamic experimental approach. Voltammetric data obtained by using a variety of forms (derived from charge-transfer type interactions) of iodide implicate the triiodide ion as the charge carrier accounting for the diffusion-limited voltammetric response whereas the charge transport of iodide seems to be limited by transmembrane diffusion. The data are used to support one of the many proposed mechanisms for conductance of iodide in membranes.     

Platinum-catalyzed intramolecular hydroamination of unactivated olefins with secondary alkylamines

Reaction of benzyl-2,2-diphenyl-4-pentenylamine with a catalytic 1:2 mixture of [PtCl2(H2C=CH2)]2 (2.5 mol %) and PPh3 in dioxane at 120 degrees C for 16 h led to isolation of 1-benzyl-2-methyl-4,4-diphenylpyrrolidine in 75% yield. A number of gamma- and delta-amino olefins underwent intramolecular hydroamination to form the corresponding pyrrolidine derivatives in moderate to good yield. The reaction displayed excellent functional group compatibility and low moisture sensitivity.     

The role of MgO in the binding of SO<Subscript>2 </Subscript>by lime-containing materials

Summary The results of investigation of MgO participation in the binding of SO₂ with lime-containing materials as sorbents are presented. Experiments of SO₂ binding into solid phase using model samples of reactive grade MgO and CaO varying the mole ratio of MgO/CaO from 9:1 to 1:9 were carried out. Besides, dolomite and limestone samples with different MgO/CaO mole ratio (from 1.24 to 0.13) and samples of ashes formed at combustion of Estonian oil shale (containing 35-40% of carbonates) and its semicoke were studied Initial samples, intermediate and final products were subjected to chemical, IR-spectroscopy, X-ray and BET specific surface area analyses. The results of the present study confirmed the active participation of MgO in the binding of SO₂ into the solid phase. In addition to CaSO₄ the formation of Ca,Mg-double sulphate CaMg₃(SO₄)₄ and -MgSO₄ was observed. The presence of CaMg₃(SO₄)₄ was fixed in a large temperature range 400-900°C and that of -MgSO₄ in between 500-700°C. The optimum temperature range for formation and durability of CaMg₃(SO₄)₄ was 700-800°C.